Oil Mallee Farming Optimization Problem

Farmer Joe is considering plant mallees (a type of eucalyptus) on part of his 90 hectares of land. Wheat profits is $120/ha, while mallee profit is $90/ha. He also knows that mallees will cost him 2 days of work/ha, while wheat costs 3 days/ha. He is a profit-maximizing farmer who has a maximum of 180 working days available (labor constraint).

Use the sliders to explore how changing the Mallee area constraints and the labor constraint affects the feasible area for a solution to Joe's problem.

Use the "profit" slider to explore how much profit Joe could possibly make, while staying within the feasible solution region.

Can you see at which basic solution corner his profit-maximizing solution exist? What are the limiting constraints?

What is the characteristic of the optimal solution indicated by a black circle?

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The problem setup is where X1 is wheat area and X2 is the Mallee area:

Maximize

subject to:

;

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This problem is based on real-life decision problems that farmers in Western Australia have to make. Oil mallee farming is emerging as a potential addition to dry-land agriculture systems. Planting mallees can generate income from carbon credits, from biofuels, and may also come with additional environmental benefits that improve farming practice.

Of course, the on-farm economics is very important to landholders when they decide whether to plant mallees or not, because there are costs associated with the initial plantings and they essentially take cropping land out of production.